Second-order spectral local isotropy in turbulent scalar fields
- 11 April 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 80 (4), 609-615
- https://doi.org/10.1017/s0022112077002389
Abstract
This work was motivated by recent experimental results on the spectra of fluctuating temperature gradients in a heated turbulent boundary layer obtained by Sreenivasan, Danh & Antonia. Standard techniques of turbulence theory are used herein to derive expressions relating the individual one-dimensional spectra of each of the three components of the spatial gradient ∂θ/∂xiin a locally isotropic turbulent scalar field. The results of the isotropic theory explain all of the new observed features of the temperature-gradient spectra. The spectra of ∂θ/∂yand ∂θ/∂zdecrease monotonically with increasing wavenumber, in contrast to the well-known behaviour of the spectrum of ∂θ/∂x, which reaches a maximum value at roughly one-tenth the Kolmogorov wavenumber. The spectra of ∂θ/∂yand ∂θ/∂zare relatively rich in low frequency energy and relatively poor in high frequency energy compared with the spectrum of ∂θ/∂x. The absolute magnitudes of the spectra of ∂θ/∂yand ∂θ/∂zcalculated from the spectrum of ∂θ/∂xusing the isotropic relations are in generally good agreement with the corresponding measured spectra for a large range of wavenumbers, indicating second-order spectral local isotropy of the fine-scale scalar structure for sufficiently large wavenumbers. The form of the spectra of ∂θ/∂yand ∂θ/∂zin the inertial subrange is derived analytically.Keywords
This publication has 3 references indexed in Scilit:
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- Structure of Temperature Fluctuations in the Turbulent Wake behind a Heated CylinderPhysics of Fluids, 1971
- Measurements of spectral energy transfer in grid turbulenceJournal of Fluid Mechanics, 1969